A security analyst is verifying a property of an encryption key generation algorithm. The analyst needs to prove the following statement:

'For every non-zero rational number $α\alpha$ and every irrational number $β\beta$ , the result of the calculation $5αβ\frac{5\alpha}{\beta}$ is always an irrational number.'

Identify the correct starting assumption for a proof by contradiction of this statement.

There exists a non-zero rational number $α\alpha$ and an irrational number $β\beta$ such that $5αβ\frac{5\alpha}{\beta}$ is rational.
For all non-zero rational numbers $α\alpha$ and all irrational numbers $β\beta$ , the value $5αβ\frac{5\alpha}{\beta}$ is rational.
There exists a non-zero rational number $α\alpha$ and an irrational number $β\beta$ such that $5αβ\frac{5\alpha}{\beta}$ is irrational.
For all non-zero rational numbers $α\alpha$ and all irrational numbers $β\beta$ , the value $5αβ\frac{5\alpha}{\beta}$ is irrational.

A security analyst is verifying a property of an encryption key generation algorithm. The analyst needs to prove the following statement:

'For every non-zero rational number $α\alpha$ and every irrational number $β\beta$ , the result of the calculation $5αβ\frac{5\alpha}{\beta}$ is always an irrational number.'

Identify the correct starting assumption for a proof by contradiction of this statement.

There exists a non-zero rational number $α\alpha$ and an irrational number $β\beta$ such that $5αβ\frac{5\alpha}{\beta}$ is rational.
For all non-zero rational numbers $α\alpha$ and all irrational numbers $β\beta$ , the value $5αβ\frac{5\alpha}{\beta}$ is rational.
There exists a non-zero rational number $α\alpha$ and an irrational number $β\beta$ such that $5αβ\frac{5\alpha}{\beta}$ is irrational.
For all non-zero rational numbers $α\alpha$ and all irrational numbers $β\beta$ , the value $5αβ\frac{5\alpha}{\beta}$ is irrational.

1.1 Proof by Contradiction

Question 18

Markscheme

1.1 Proof by Contradiction

Question 18

Markscheme

1.1 Proof by Contradiction

Question 18

1.1 Proof by Contradiction Questions

1.1 Proof by Contradiction

Question 18

1.1 Proof by Contradiction Questions